1. Field of the Invention
The present invention relates to phase-matched high-order harmonic generation of soft and hard X-rays using infrared driving lasers in a high-pressure non-linear medium. In particular, the present invention relates to efficient generation of coherent x-ray radiation by coherent upconversion of light from an intense mid-infrared pulsed laser in a high pressure gas nonlinear medium. The invention further relates to a general method for global optimization of the flux of coherent light of desired wavelength by selecting the optimal wavelength of the driving laser and its parameters, in combination with the optimal nonlinear medium and its parameters.
2. Background of the Invention
High-order harmonic generation (HHG) is a unique source of femtosecond-to-attosecond duration soft x-ray beams that has opened up new studies of atoms, molecules, and materials, as well as enabling new high-resolution coherent imaging using a table-top light source. To date, however, most applications of HHG radiation employ extreme ultraviolet wavelengths (photon energy ˜20-100 electron volts), because the efficiency of the HHG process decreases rapidly at higher photon energies. This decrease is not fundamental to the HHG process, but rather results from the large phase mismatch between the generated HHG field and the driving laser field at 800 nm, which to date is used in nearly all HHG experiments because of the availability of high-power ultrashort pulse lasers generating light at this wavelength. The obstacle in phase-matching HHG upconversion to very short wavelengths is the higher required laser intensity, which results in high levels of ionization and thus large free electron dispersion. This dominant plasma dispersion limits phase matching of HHG to relatively low levels of ionization, where neutral atom dispersion can balance the anomalous free-electron plasma dispersion. For a 0.8 μm driving laser, the “critical” ionization levels above which true phase matching is not possible are ≈5% for argon and ≈0.5% for helium. As a result, the highest photon energies that can be phase matched in Ar and He are ˜50 eV and ˜130 eV respectively.
Another important limit in HHG is the highest photon energy that can be generated by the laser regardless of phase matching—the so-called cutoff energy. This cutoff is given by hνmax=Ip+3.2Up, where Ip is the ionization potential of the gas and Up∝ILλL2 is the quiver energy of the liberated electron, λL is the wavelength of the laser driving the process, and IL is its intensity. The favorable λL2 scaling has motivated studies of HHG with mid-infrared driving pulses with wavelength longer than 800 nm. Significant extension of the cutoff energy hνmax to higher energy was demonstrated in several experiments. However, it was recently found theoretically that the actual EUV or x-ray yield of an atom radiating HHG light scales as λL−5.5±0.5. The use of a longer wavelength driver, although it increases the energy of the individual HHG photons, greatly reduces the total conversion efficiency and thus the total energy in the burst of HHG photons [6]. Thus, increasing the HHG yield by finding new methods of phase-matching the conversion process is critical to obtain a usable flux at shorter wavelengths.
It is an object of the present invention to generate high-order harmonic light in the soft and hard X-ray regions of the spectrum in a more-efficient manner that optimizes phase matching of the light. This can be accomplished by using a mid-infrared driving laser in combination with a very high-pressure non-linear medium. This method of optimizing efficiency of high-harmonic generation conversion to short wavelengths has not heretofore been recognized. Past teaching in the area of high-order harmonic generation mostly employed sub-atmosphere target pressures, with the use of a very short-wavelength driving laser to maximize high-harmonic flux.